Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<int> res;
int main() {
  int n;
  cin >> n;
  for (int k1 = 1; (k1 * k1 + k1) <= 2 * n; k1++) res.push_back(k1 * k1 + k1);
  int m = res.size();
  for (int i = 0; i < m; i++) {
    int l = 0, r = m - 1, mid;
    while (r - l > 1) {
      mid = (r + l) / 2;
      if (res[i] + res[mid] > 2 * n)
        r = mid;
      else
        l = mid;
    }
    if (res[i] + res[l] == 2 * n || res[i] + res[r] == 2 * n) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}